There is an interesting study in contrasts in my group going on at the moment.
Shodokan people tend to be very quick on their feet both attacking and defending. It's how we train, its what we like to do. A while back a Nidan from an (yes I'm being coy) Aikikai sensei whose primary fame is in the West joined our group. He is a study in opposite. Some would call him rooted - I call him heavy.
I really think the question is not so much speed but lightness. Have that and you will have both quickness and timing.